Digital Subscriber Line (DSL) is a technology that provides high-speed communications using telephone lines. The technique requires the use of a wide band of frequencies to send more information than conventional voice calls require. Wideband modulation schemes need to take into account the broadband characteristics of the medium used to communicate. Twisted pair copper wire subscriber loops used to provide access to the local exchange in telephone circuits exhibit frequency dependent attenuation, with higher frequencies suffering more attenuation than the lower ones. Further, these subscriber loops also exhibit a non-linear phase response with frequency, with the lower frequencies exhibiting more non-linearity. This kind of channel characteristic results in the dispersion of an impulse, sent by the transmitter, at the receiver, thus corrupting the reception. This dispersion, also referred to as inter-symbol interference (ISI), results in data loss and hence, loss of communication reliability.
A channel's limited bandwidth has a dispersive effect on the transmitted pulse. High-frequency loss in the channel tends to reduce the slope of the pulse edges resulting in finite rise times (precursor distortion). At low frequencies, the nonlinear phase characteristics tend to produce a long decay tail (postcursor distortion), resulting in a smeared pulse shape. The “available” bandwidth and the phase characteristics of a channel are solely a function of the medium used. Distortion suffered by a given pulse results in interference to its neighbors in time. A given pulse is distorted by the presence of tails from past pulses and precursors of future pulses. This effect is known as inter-symbol interference (ISI). Thus, at the receiver, detection of symbols is further complicated by the presence of pulse distortion in addition to noise. For a given channel, since the channel attenuation and noise characteristics can be determined a priori, ISI can be eliminated by predicting the channel's future and past influence on any received symbol. The process of eliminating ISI from the received data is referred to as equalization.
Discrete multi-tone modulation (DMT) is an orthogonal frequency-division multiplexing (OFDM) technique. It was introduced by Ebert and Weinstein and later improved by Peled and Ruiz to take advantage of digital signal processors and fast Fourier transform (FFT) processes. DMT is generally used to refer to an FFT-based multi-carrier modulation scheme for high-speed data transmission in a wired environment such as the digital subscriber line (DSL). A host of high-speed transmission standards such as ADSL (Asymmetric DSL), HDSL (High-speed DSL), VDSL (Very high-speed DSL), and so on use DMT as the modulation technique.
Discrete multi-tone modulation is based on modulating bits on a sequence of N baseband tones (also known as sub-channels or bins), generally evenly spaced. Modulation involves mapping the bi bits in the ith bin to a complex number chosen from a corresponding 2bi QAM (quadrature amplitude modulation) constellation. The modulated bins and the corresponding complex conjugate bins are then inverse Fourier transformed (IFFT) to generate 2N real time samples constituting a symbol. Thus for a baseband system of total allowed bandwidth W, the symbol time is 2N/2W=1/fc for the case of Nyquist sampling where fc is the frequency spacing between bins. For example, the ADSL standard uses N=256 bins that span a bandwidth of 1.104 MHz resulting in a frequency spacing of 4.3125 kHz. AT&T Corporation has been developing its version of DMT-based DSL technology called the Tethered Virtual Radio Channel (TVRC).
Referring briefly to FIG. 5, there is shown a block schematic diagram of a conventional TVRC modem which may be located either at a telephone central office (CO) or as customer premises equipment (CPE). A difference between the CO TVRC modem and a CPE TVRC modem is that the CPE modem receives its clock from the CO modem.
TVRC differentiates itself from ADSL by offering duplex T1-like service for loops up to twelve thousand feet of twenty six gauge (AWG) wire cable pairs and graded service for longer lengths. TVRC, like ADSL, uses DMT as the baseband modulation scheme. The Multiple Turbo Trellis coded modulation (MTTCM) scheme of inner coder 510 developed by AT&T gives a significant signal-to-noise ratio (coding gain) advantage over the Wei coder recommended in the standards for constellation sizes from 4 to 256 with the largest gains for QPSK. Further, unlike ADSL, TVRC is a full-band duplex communication system using the same band for both upstream and downstream communications. It may or may not be symmetric depending on the channel conditions that determine the bit and power allocation profiles for the up and downstream channels. The outer coder 505 is the standards recommended Reed-Solomon coder with the design chosen to maintain error levels at one in 109 bits. The digital broadband Echo Canceller 535 developed for the duplex channel along with the analog hybrid ensures echo-interference-free duplex communications.
Bit distribution in each sub-channel is determined from the channel attenuation and noise characteristics measured during initialization using a known pseudo-random (PN) sequence. The well-known water-pouring algorithm of adding power proportional to the channel terrain has been modified by Sonalkar and Sankaranarayanan as a constrained allocation of bits and hence, power subject to a total power budget of 100 mW and a power spectral mask constraint defined by the Federal Communications Commission for the Asymmetric Digital Subscriber Line (ADSL) standards. A computationally fast algorithm using bit removal instead of bit-by-bit allocation has been adopted. Channel attenuation is measured at the receiver as the ratio of the received PN sequence to the known transmitted sequence and the noise profile is measured at the receiver with the transmitter silent. Duplex versions of the above algorithm have also been developed by Sonalkar et al. to solve the problem of joint bit allocations to the upstream and downstream channel. The information on the bit and power profile is communicated back to the transmitter by the receiver during initialization.
The incoming bit stream at the transmitter 500 after scrambling is Reed-Solomon (RS) encoded. The RS encoder 505 used is a (136, 136-R) coder where 136 is an example of the number of output bytes and R is twice the number of symbols that can be corrected. The choice of R determines the effective system bit error rate (BER) for a given inner coder BER. The RS coder 505 in the TVRC transmitter design of FIG. 5 uses a symbol of length 8 bits, i.e., a byte. The 136-byte output of the RS encoder 505 results in an input block of 1088 bits to the Turbo encoder 510. The Turbo encoder 510 uses the bit allocation profile to map bi bits at a time from the incoming bit stream, encode them with the appropriate number of parity bits and map the resultant bits to a complex number from a 256-point constellation. When all B=Σbi, where i=1, 2, . . . , 256, total bits per symbol are read, the bit table is reset to the start to continue encoding the Turbo input block of 1088 bits until no more bits are left to encode. The bins with no bits are not modulated, i.e., zero power is sent on such bins. The result is a continuing vector of complex values which when taken 256 at a time, scaled by the appropriate power values, complex conjugated and inverse fast Fourier transformed (IFFT) at IFFT 520 yields a 512-point vector of time samples.
Prefixing the last 32 time samples of the 512-sample frame to the start of the frame ensures that for a shortened 32-tap channel the data appears periodic to the channel and thus, at the receiver, the frequency bins of the prefix discarded 512-sample FFT will remain orthogonal. If x(n) is an N-sample vector transmitted with a CP-sample cyclic prefix, h(n) is the channel response, and X(n) and H(n) are the discrete Fourier transforms of x(n) and h(n) respectively, then at the receiver, the discrete transform relationship:
                              x          ⁡                      (            n            )                          *                                            h              ⁡                              (                n                )                                      ⁢                          ⟷                                                                                ⁢                FFT                ⁢                                                                                        ⁢                          X              ⁡                              (                n                )                                              ·                      H            ⁡                          (              n              )                                                          (        1        )            holds iff x(n) is either an infinite sequence of samples (infinite block length) or if x(n) is periodic with period N. Constraining the channel to be non-zero for only CP-samples and using a cyclic prefix of length CP for each block N samples result in the data appearing periodic to the channel, thus eliminating receiver inter channel interference (ICI) as shown subsequently herein. Interpolation and parallel-to-serial conversion of the time samples followed by digital to analog conversion completes the processing of data at the transmitter.
At the receiver 550, the digitized data coming through the hybrid 540 and the analog front end is decimated down to baseband. The decimated time samples are buffered 544 (N+CP) at a time and digitally filtered with the time domain equalizer (TEQ) 560 determined during initialization to shorten the channel to 32 or less taps. For a duplex system, echo cancellation via echo canceller 535 is done to eliminate the echo leakage from the transmitter 500. This is followed by the removal of the cyclic prefix of 32 samples. An FFT 575 of the remaining 512 samples results in a vector of 256 complex values and their conjugates in the frequency domain. The complex frequency values are then scaled by an appropriate vector of complex numbers that ensures phase and power equalization of the received signal. This frequency domain equalizer (FEQ) 580 is also determined during initialization and equalizes (cancels) the phase distortion and power attenuation introduced by the channel. The equalized complex numbers are then fed to the Turbo decoder 585. Reed-Solomon decoding and de-scrambling via decoder 590 completes the receiver data processing and the resulting bits are streamed as appropriate for the application.
The two ends of a typical subscriber line connection are the customer premises equipment (CPE) and the local exchange also known as the central office (CO). The CPE and CO are sample and frame synchronized with each other after the CPE synchronizes its clock to the master CO clock during initialization. Downstream is the direction from the CO to the CPE and upstream indicates the reverse direction from the subscriber to the central office. Timing recovery at the CPE is done during the initial handshaking and from then on synchronization is maintained by constantly updating the parameters with the reception of the PN sequence sent as a 69th frame after successive 68 frames of data transmission. If required, the 69th PN frame on time-averaging, also helps adapt and update the channel-dependent parameters like the TEQ 560, the FEQ 580, the echo canceller (EC) 535, and bit and power allocation profiles. One technique for adaptively updating the channel parameters and constantly monitoring the channel is referred to as the Auto-Configuration Protocol and is one algorithm developed by members of AT&T Labs-Research that may be utilized with the present invention. Other techniques for updating channel parameters and monitoring a channel may be likewise utilized with the present invention.
Inter-symbol interference (ISI, distortion in the time-domain) and inter-channel interference (ICI, distortion in the frequency domain, also known as inter-bin interference) cause corruption of data sent over long twisted pair copper wires connecting CPE and CO. A channel's limited bandwidth causes distortion in the transmitted pulse. High-frequency loss reduces the slope of the pulse edges resulting in precursor distortion and low frequencies nonlinear channel phase response results in a long pulse tail causing postcursor distortion. This distortion creates interference in the preceding and following pulses, thus complicating the problem of symbol detection in this challenging subscriber loop environment (mixed gauges, bridge taps, noise ingress in the upstream direction among other known problems).
In DMT-based modulation for a DSL system, a pulse (symbol) is typically 512-samples long preceded by a cyclic prefix (length CP in general) of the last 32 samples of the current frame. The cyclic prefix is used to provide time domain separation of adjacent symbols. Each time domain symbol at the transmitter is the inverse Fourier transform of a band of 256 independent frequencies (bins) modulated using the parameters determined during initialization. At the receiver 550, the received time domain samples are collected a frame at a time. A Fourier transform 575 is then used to recover data in the original 256 frequency bins. If the channel impulse response is longer than 32 taps (the size of the cyclic prefix), ISI between adjacent symbols results in a loss of orthogonality between the channels (bins) in the band of modulation, and the result is ICI. Detection based on an assumption of orthogonal channels within the band no longer holds, and performance (i.e. bit error rate, data throughput) suffers.
Theoretical considerations for shortening impulse response are discussed in Melsa et al., “Impulse Response Shortening for Discrete Multitone Transceivers”, published in IEEE Transactions for Communications, Vol. 44, No. 12, December, 1996, incorporated by reference as to its entire contents. While Melsa et al. provide a theoretical framework for our invention, this prior work failed to, for example, appreciate, disclose or suggest the computation of all eigenvalues and the determination of the smallest eigenvalue as taught by our invention, perhaps, because they perceived that the complexity of the computations precluded them from doing so or they never recognized the possibility. Nevertheless, as discussed herein, we have used this optimal strategy and reduced the complexity of the algorithm.
Thus, to maintain reliable communications at a desired error rate and data rate, it is important to minimize the ISI. This process of eliminating or minimizing ISI in time is referred to as time domain equalization and involves reversing the effects of the long dispersive channel. For the case of DMT-based DSL modems, equalization refers to the shortening of the measured channel at the receiver with a filter computed during the initial handshaking between the modem at the Central Office (CO) and the DSL modem at the customer premises. Shortening the channel to the length of the cyclic prefix which separates adjacent symbols eliminates ISI completely for the ideal case of an infinite length TEQ, but reduces it to the minimum possible for a finite filter tap length. An optimal linear solution for computing this finite length TEQ filter involves determining the smallest eigenvalue and eigenvector of a real, symmetric matrix. While theoretically this solution is optimal, the choice of the implementation technique determines the accuracy of the filter designed, and therefore, the overall system reliability.